How to hide the armature to do UV unwrapping?
You could use one of two approaches to do this.


Layers
Object Hiding


Layers

This is what I would recommend.

Layers let you control at what level an object is "visible" much like a layer in a program like photoshop. You can enable or disable layers and move objects to different layers. To move an object to another layer you only have to use the M key by default

Simply select your Armature object(s) and hit M then you can move to any of the layers you want. The little orange dot in the layer selector shows which layer the active object is on.

You can read more about layers here and since you might be new, it is very good to understand how they make working with blender easier.

Object Hiding

If for some reason you cannot use layers, you can hide the objects you do not want to see while not moving them to another layer. You can do this by selecting the object(s) you want to hide and pressing H.

Once this is done you can no longer see / select the object from the 3d view. The object will still show up in renders.

If you want to see all the objects you have hidden, you can press Alt + H. 

If you only want to unhide specific objects, you can use the outliner (the tree view in the top right) and click on the eye icon to unhide hidden objects.

You can also use other shortcuts to hide objects en masse etc. This post also details one way you can hide all objects EXCEPT the selected object

Comments:

You can use both object hiding and layers together but turning off a layer makes it get hidden from rendering.

Hiding an object but keeping its layer visible does not make hide it from rendering.